We test the performance of fGOT on a graph alignment and community detection task in structured graphs. We consider two experimental settings: the comparison of a graph with a noisy version of the same graph, and its comparison with a random structured graph.
We show the results obtained by GW (as described in the previous section) and by the MGD and the stochastic MGD version of fGOT for three different graph filter models. Namely \(g(L) = \sqrt{L^{\dagger }}\) , which corresponds to the approximated version of the original GOT distance for smooth signals [1]}, and two heat kernel distances: \(g(L) = e^{-0.2 L}\)  and \(g(L) = e^{-0.8 L}\) .
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